The 19-year-old McIlroy held a four-stroke lead going into the final round, but bogeyed two of the first three holes and then missed a five-foot putt for victory on No. 18 to settle for a 71. He then missed a 1-footer and made bogey on the second playoff hole before Lucquin holed a 12-footer for his first European Tour win in his 175th attempt.
"I was very nervous on the first tee but I was confident in my swing," the 29-year-old Lucquin said. "When I holed that putt, my wife and little boy ran on the green and when I saw them, it was a dream."
Lucquin shot a 67 to tie McIlroy at 13-under 271.
Both players parred the 18th on the first playoff hole after missing birdie putts, Lucquin from 25 feet and McIlroy from 12 feet.
Miguel Jimenez (67), Gary Orr (67), Julien Clement (68) and Christian Cevaer (68) shared third at 12 under.
Lucquin's first victory beat his previous best result of second place in last year's Malaysian Open.
McIlroy looked to be in control after he sank a 15-foot birdie putt at the long 15th hole to take back the lead, but he parred the next two before his bogey at the last.
"Obviously I am very disappointed," McIlroy said. "I didn't make it easy for myself starting off but then I thought I battled back really well."
McIlroy had led since his opening-round 63 on Thursday.
"I can take a lot from this week. I played well all week and played well coming down the stretch," he said. "I came here after three missed cuts in a row and found a bit of form but it would have been nice to go home with the trophy."